Question

Prove that the associative property hold true for the addition $(\frac{7}{8}+\frac{2}{5})+\frac{8}{3}$

Answer 1

$\begin{array}{c}\text{Here}\\ \left(\frac{7}{8}+\frac{2}{5}\right)+\frac{8}{3}=\left(\frac{35+16}{40}\right)+\frac{8}{3}\\ =\frac{51}{40}+\frac{8}{3}\\ =\frac{103+320}{120}\\ =\frac{423}{120}\\ Now,\\ \frac{7}{8}+\left(\frac{2}{5}+\frac{8}{3}\right)\\ =\frac{7}{8}+\left(\frac{6+40}{15}\right)\\ =\frac{7}{8}+\frac{41}{15}\\ =\frac{105+328}{120}\\ =\frac{433}{120}\\ \text{Hence the both value are equal}\\ \therefore \text{it holds associative property}.\end{array}$